The flash duration (or the time there is light being emitted from the flash tube) can be as fast as 1/13000s. When this is the sole light source, this will freeze action well.
However, you are still limited to your sync speed. If you have a significant amount of light at 1/200s, that light can still cause blur, if the movement is fast enough.
With all settings the same, any blur that would be present without the flash, would be present with the flash as well.
If your camera's x-syncs speed is 1/500, then our remotes can trigger fast enough to sync. In fact, they can sync up to 1/2500s,
if the camera's x-sync speed is that high. Our remotes and lights, however, cannot sync faster than any camera's x-sync speed. To my knowlege, no studio lights can truly High SpeedSync, and the remotes that claim to force some lights to do this are fraught with inconsistencies and compromises.
There are further discussions on sync speed in these two threads:
viewtopic.php?f=8&t=66 viewtopic.php?f=8&t=67